Quasi-linearizability of various benchmark control mechanical systems

A mechanical system is said to be quasi-linearizable if there is a linear transform of velocity that eliminates all terms quadratic in the velocity from the equations of motion of the system. It is known that controller/observer design becomes tractable when the equations of motion of a mechanical system are in quasi-linearized form. In this paper, we examine quasi-linearizability of the following seven benchmark control mechanical systems: a planar PPR robot, the inverted pendulum on a cart, the TORA system, the mass-beam system, the Furuta pendulum, the Pendubot/Acrobot system, and a magnetic suspension system. We show that the first three of them are quasi-linearizable and the rest are not. We envision that this result will be useful in controller/observer synthesis for those quasi-linearizable systems.